Odds of flopping two pair in Hold 'Em

[BlawBlaw]

I found on a web site that the odds of flopping two pair with a non pocket pair hand is 2.02 (48.5-to-1). I was just curious as to how this was determined mathematically.

[AaronBrown]

To flop two pair without a pair in hand, you need one card on the flop to match the higher card in your hand, one to match the lower card, and one to be any of the 44 cards in the eleven other ranks (or you would have a full house).

There are three candidates for the first card, three for the second and 44 for the third, that's 3*3*44 = 396. There are 50*49*48/(3*2*1) = 19,600 ways to flop. This calculation is so useful, it is written C(50,3), pronounced "50 choose 3." You can also do COMBIN(50,3) in Excel.

396/19,600 = 0.0202 or 1 in 49.49, which is 48.49 to 1.

[BabyJesus]

The real point is. If I can flop a full house or quads with it, I'll play it.